Structure in the Spectra of Some Multiplier Algebras

2014 ◽  
pp. 177-200
Author(s):  
Richard Rochberg
Keyword(s):  
Multiplier Algebras

Banach Algebras whose Duals are Multiplier Algebras

1981 ◽  
Vol 13 (1) ◽  
pp. 66-68 ◽  
Author(s):  
E. O. Oshobi ◽  
J. S. Pym
Keyword(s):  
Banach Algebras ◽  
Multiplier Algebras

Invertible Factorization over Multiplier Algebras

2012 ◽  
Vol 75 (2) ◽  
pp. 151-164 ◽  
Author(s):  
Tavan T. Trent
Keyword(s):  
Multiplier Algebras

Hilbert \(C^{*}\)-modules in which all relatively strictly closed submodules are complemented

2021 ◽  
Vol 56 (2) ◽  
pp. 343-374
Author(s):  
Boris Guljaš ◽  
Keyword(s):  
Hilbert Space ◽  
Hilbert Modules ◽  
Strict Topology ◽  
Direct Sums ◽  
Essential Ideal ◽  
Closed Submodule ◽  
Closed Submodules ◽  
Hereditary Algebras ◽  
Multiplier Algebras

We give the characterization and description of all full Hilbert modules and associated algebras having the property that each relatively strictly closed submodule is orthogonally complemented. A strict topology is determined by an essential closed two-sided ideal in the associated algebra and a related ideal submodule. It is shown that these are some modules over hereditary algebras containing the essential ideal isomorphic to the algebra of (not necessarily all) compact operators on a Hilbert space. The characterization and description of that broader class of Hilbert modules and their associated algebras is given. As auxiliary results we give properties of strict and relatively strict submodule closures, the characterization of orthogonal closedness and orthogonal complementing property for single submodules, relation of relative strict topology and projections, properties of outer direct sums with respect to the ideals in \(\ell_\infty\) and isomorphisms of Hilbert modules, and we prove some properties of hereditary algebras and associated hereditary modules with respect to the multiplier algebras, multiplier Hilbert modules, corona algebras and corona modules.

scholarly journals Norms of inner derivations for multiplier algebras of C⁎-algebras and group C⁎-algebras

2012 ◽  
Vol 262 (5) ◽  
pp. 2050-2073 ◽  
Author(s):  
Robert J. Archbold ◽  
Eberhard Kaniuth ◽  
Douglas W.B. Somerset
Keyword(s):  
Multiplier Algebras

ON BOHR'S INEQUALITY

2002 ◽  
Vol 85 (2) ◽  
pp. 493-512 ◽  
Author(s):  
VERN I. PAULSEN ◽  
GELU POPESCU ◽  
DINESH SINGH
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Banach Algebras ◽  
Equivalent Norm ◽  
C Algebra ◽  
Theoretic Proof ◽  
Higher Dimensional ◽  
Bohr’S Inequality ◽  
Kernel Hilbert Spaces ◽  
Multiplier Algebras

Bohr's inequality says that if $f(z) = \sum^{\infty}_{n = 0} a_n z^n$ is a bounded analytic function on the closed unit disc, then $\sum^{\infty}_{n = 0} \lvert a_n\rvert r^n \leq \Vert f\Vert_{\infty}$ for $0 \leq r \leq 1/3$ and that $1/3$ is sharp. In this paper we give an operator-theoretic proof of Bohr's inequality that is based on von Neumann's inequality. Since our proof is operator-theoretic, our methods extend to several complex variables and to non-commutative situations.We obtain Bohr type inequalities for the algebras of bounded analytic functions and the multiplier algebras of reproducing kernel Hilbert spaces on various higher-dimensional domains, for the non-commutative disc algebra ${\mathcal A}_n$, and for the reduced (respectively full) group C*-algebra of the free group on $n$ generators.We also include an application to Banach algebras. We prove that every Banach algebra has an equivalent norm in which it satisfies a non-unital version of von Neumann's inequality.2000 Mathematical Subject Classification: 47A20, 47A56.

scholarly journals On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces

2017 ◽  
Vol 69 (1) ◽  
pp. 54-106 ◽  
Author(s):  
Michael Hartz
Keyword(s):  
Hilbert Spaces ◽  
Special Class ◽  
Reproducing Kernel ◽  
Reproducing Kernels ◽  
Isomorphism Problem ◽  
Reproducing Kernel Hilbert Spaces ◽  
Universal Space ◽  
Kernel Hilbert Spaces ◽  
Arveson Space ◽  
Multiplier Algebras

AbstractWe continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with the restrictions of a universal space, namely theDrury-Arveson space. Instead, we work directly with theHilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of complete Nevanlinna-Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic.This generalizes results of Davidson, Ramsey,Shalit, and the author.

scholarly journals Multipliers on vector spaces of holomorphic functions

2000 ◽  
Vol 159 ◽  
pp. 167-178 ◽  
Author(s):  
Hermann Render ◽  
Andreas Sauer
Keyword(s):  
Uniqueness Theorem ◽  
Complex Plane ◽  
Hadamard Product ◽  
Holomorphic Functions ◽  
Vector Spaces ◽  
Spaces Of Holomorphic Functions ◽  
Coefficient Multipliers ◽  
Multiplier Algebras

Let G be a domain in the complex plane containing zero and H(G) be the set of all holomorphic functions on G. In this paper the algebra M(H(G)) of all coefficient multipliers with respect to the Hadamard product is studied. Central for the investigation is the domain introduced by Arakelyan which is by definition the union of all sets with w ∈ Gc. The main result is the description of all isomorphisms between these multipliers algebras. As a consequence one obtains: If two multiplier algebras M(H(G1)) and M(H(G2)) are isomorphic then is equal to Two algebras H(G1) and H(G2) are isomorphic with respect to the Hadamard product if and only if G1 is equal to G2. Further the following uniqueness theorem is proved: If G1 is a domain containing 0 and if M(H(G)) is isomorphic to H(G1) then G1 is equal to .

scholarly journals Rigidity theory for C∗-dynamical systems and the “Pedersen rigidity problem”

2018 ◽  
Vol 29 (03) ◽  
pp. 1850016 ◽  
Author(s):  
S. Kaliszewski ◽  
Tron Omland ◽  
John Quigg
Keyword(s):  
Fixed Point ◽  
Abelian Group ◽  
Dynamical Systems ◽  
Dual Group ◽  
Locally Compact Abelian Group ◽  
Alternative Formulation ◽  
Crossed Products ◽  
Locally Compact ◽  
Fixed Point Algebra ◽  
Multiplier Algebras

Let [Formula: see text] be a locally compact abelian group. By modifying a theorem of Pedersen, it follows that actions of [Formula: see text] on [Formula: see text]-algebras [Formula: see text] and [Formula: see text] are outer conjugate if and only if there is an isomorphism of the crossed products that is equivariant for the dual actions and preserves the images of [Formula: see text] and [Formula: see text] in the multiplier algebras of the crossed products. The rigidity problem discussed in this paper deals with the necessity of the last condition concerning the images of [Formula: see text] and [Formula: see text]. There is an alternative formulation of the problem: an action of the dual group [Formula: see text] together with a suitably equivariant unitary homomorphism of [Formula: see text] give rise to a generalized fixed-point algebra via Landstad’s theorem, and a problem related to the above is to produce an action of [Formula: see text] and two such equivariant unitary homomorphisms of [Formula: see text] that give distinct generalized fixed-point algebras. We present several situations where the condition on the images of [Formula: see text] and [Formula: see text] is redundant, and where having distinct generalized fixed-point algebras is impossible. For example, if [Formula: see text] is discrete, this will be the case for all actions of [Formula: see text].

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